Vital statistics | Pele | Laka | Akea | Kapo | Lono | Namaka

Vital statistics

Comma c = 5120/5103

7-limit minimax: 3 and 7 1/7c sharp, 5 just
[|1 0 0 0>, |10/7 1/7 1/7 -1/7>,
|0 0 1 0>, |10/7 -6/7 1/7 6/7>]
Eigenmonzos: 2, 5/4, 7/6

9-limit minimax: 3 1/8c sharp, 5 just, 7 1/4c sharp
[|1 0 0 0>, |5/4 1/4 1/8 -1/8>,
|0 0 1 0>, |5/2 -3/2 1/4 3/4>]
Eigenmonzos: 2, 5/4, 9/7

Lattice basis: 3/2 length 0.5670, 10/9 length 1.8063
Angle(3/2, 10/9) = 82.112 degrees
Map to lattice: [<0 1 2 -4|, <0 0 1 1|]

Map: [<1 0 0 10|, <0 1 0 -6|, <0 0 1 1|]
Generators: 2, 3, 5
EDOs: 99, 140, 239, 292, 391, 490, 881bd
Badness: 0.000153

Projection pairs: 7 5120/729

Music

By Gene Ward Smith
Choraled play
By Chris Vaisvil
Hemifamity27

Pele

Commas: 441/440, 896/891

Minimax tuning
[|1 0 0 0 0>, |17/10 0 1/10 0 -1/10>,
|17/5 -2 6/5 0 -1/5>,
|16/5 -2 3/5 0 2/5>, |17/5 -2 1/5 0 4/5>]
Eigenmonzos: 2, 10/9, 11/9

Lattice basis: 3/2 length 0.3812 56/55 length 1.5893
Angle(3/2, 56/55) = 90.4578 degrees
Map to lattice: [<0 1 4 -2 -6|, <0 0 -1 -1 -1|]

Map: [<1 0 0 10 17|, <0 1 0 -6 -10|, <0 0 1 1 1|]
Generators: 2, 3, 5
Edos: 41, 46, 77e, 87, 99e, 128, 145, 186e, 232, 285e, 331e
Badness: 0.000648

Projection pairs: 7 5120/729 11 655360/59049

13-limit

Commas: 196/195, 352/351, 364/363

13-limit minimax
Eigenmonzos: 2, 10/9, 13/10

15-limit minimax
Eigenmonzos: 2, 15/13, 6/5

Map: [<1 0 0 10 17 22|, <0 1 0 -6 -10 -13|, <0 0 1 1 1 1|]
EDOs: 29, 41, 46, 58, 87, 145, 232, 377cef
Badness: 0.000703

Laka

Commas: 5120/5103, 540/539

Minimax tuning
[|1 0 0 0 0>, |4/3 0 2/21 -1/21 1/21>,
|0 0 1 0 0>, |2 0 3/7 2/7 -2/7>,
|2 0 3/7 -5/7 5/7>]
Eigenmonzos: 2, 5/4, 14/11

Projection pairs: 5120/729 11 14348907/1310720

Map: [<1 0 0 10 -18|, <0 1 0 -6 15|, <0 0 1 1 -1|]
EDOs: 84, 97, 99e, 111, 121, 130, 152, 555de, 707de, 859bde

13 limit

Commas: 352/351, 540/539, 847/845

13 and 15 limit minimax tuning
[|1 0 0 0 0 0>, |13/8 -1/2 1/8 0 0 1/8>,
|13/4 -3 5/4 0 0 1/4>, |7/2 0 1/2 0 0 -1/2>,
|25/8 -9/2 5/8 0 0 13/8>,
|13/4 -3 1/4 0 0 5/4>]
Eigenmonzos: 2, 11/8, 14/13

17 limit

Commas: 352/351, 540/539, 847/845, 442/441

17-limit minimax
[|1 0 0 0 0 0 0>,
|13/12 0 0 1/12 1/6 -1/12 0>,
|-7/4 0 0 5/4 3/2 -5/4 0>,
|7/4 0 0 3/4 1/2 -3/4 0>,
|0 0 0 0 1 0 0>,
|7/4 0 0 -1/4 1/2 1/4 0>,
|35/12 0 0 23/12 5/6 -23/12 0>]
Eigenmonzos: 2, 11/8, 14/13

Map: [<1 0 0 10 -18 -13 32|,
<0 1 0 -6 15 12 -22|, <0 0 1 1 -1 -1 3|]
Generators: 2, 3, 5
Edos: 94, 111, 152, 205, 345

Akea

Commas: 385/384, 2200/2187

Minimax tuning
[|1 0 0 0 0>, |5/3 0 1/6 -1/6 0>,
|26/9 0 13/18 -7/18 -1/3>,
|26/9 0 -5/18 11/18 -1/3>,
|26/9 0 -5/18 -7/18 2/3>]
Eigenmonzos: 2, 14/11, 7/5

Map: [<1 0 0 10 -3|, <0 1 0 -6 7|, <0 0 1 1 -2|]
Generators: 2, 3, 5
EDOs: 34, 41, 53, 87, 140, 181, 321
Badness: 0.000998

13-limit

Commas: 325/324, 352/351, 385/384

13 and 15 limit minimax
[|1 0 0 0 0 0>, |5/3 0 1/6 -1/6 0 0>,
|26/9 0 13/18 -7/18 -1/3 0>,
|26/9 0 -5/18 11/18 -1/3 0>,
|26/9 0 -5/18 -7/18 2/3 0>,
|26/9 0 -7/9 1/9 2/3 0>]
Eigenmonzos: 2, 14/11, 7/5

Lattice basis: 3/2 length 0.5354 27/20 length 1.0463
Angle(3/2, 27/20) = 80.5628 degrees
Map to lattice: [<0 1 3 -3 1 -2|, <0 0 -1 -1 2 2|]

Map: [<1 0 0 10 -3 2|, <0 1 0 -6 7 4|, <0 0 1 1 -2 -2|]
Generators: 2, 3, 5
EDOs: 7, 41, 46, 53, 87, 94, 140, 181, 321, 408
Badness: 0.000822
Scales: akea46_13

Kapo

Commas: 5120/5103, 3025/3024

Minimax tuning
[|1 0 0 0 0>, |8/5 2/5 0 -1/15 -2/15>,
|14/5 6/5 0 7/15 -16/15>,
|16/5 -6/5 0 13/15 -4/15>,
|16/5 -6/5 0 -2/15 11/15>]
Eigenmonzos: 2, 11/9, 9/7

Map: [<1 0 0 10 7|, <0 1 1 -5 -2|, <0 0 2 2 -1|]
Generators: 2, 3, 128/99
EDOs: 152, 198, 239, 350, 391, 478, 589
EDOs: 41, 87, 111, 152, 239, 391
Badness: 0.000994

Lono

Commas: 176/175, 5120/5103

Map: [<1 0 0 10 6|, <0 1 0 -6 -6|, <0 0 1 1 3|]
EDOs: 7, 12, 39, 46, 53, 58, 99, 111
Badness: 0.00118

Namaka

Commas: 3388/3375, 5120/5103

Map: [<1 0 0 10 -6|, <0 2 0 -12 9|, <0 0 1 1 1|]
EDOs: 29, 53, 58, 87, 111, 140, 198
Badness: 0.00174

13-limit

Commas: 352/351, 676/675, 847/845

Map: [<1 0 0 10 -6 -1|, <0 2 0 -12 9 3|, <0 0 1 1 1 1|]
EDOs: 29, 53, 58, 87, 111, 140, 198
Badness: 0.000781